A new convention for the epithermal neutron spectrum component is formulated in this work, aimed at improving the accuracy of resonance integrals determination. The (1 + β)/(βE + E1+α ) form here proposed, is an approximating function of the epithermal neutron spectrum based upon calculations performed by the state-of-art Monte Carlo code MVP-3. Bias effects on determination of resonance integrals, due to the application of the well-known and used so far approximating functions, such as 1/E, 1/E1+α as well as the new form (1 + β)/(βE + E1+α ) are compared, where E is the neutron energy, α a shape factor, and β a new shape factor introduced in this work. The other bias effect is also investigated, which is caused by neglecting the position dependence of a neutron spectrum inside an irradiation capsule. To get a demonstration of the bias effects due to these assumptions, upon the determination of a neutron spectrum from a quantitative point of view in a practical case, the thermal neutron-capture cross section and resonance integral of 135Cs measured at a research reactor JRR-3 are re-evaluated. A superior property of the proposed new mathematical expression is discussed. The experimental method is proposed to determine the new shape factor β by a combinational use of triple flux monitors (197Au, 59Co, and 94Zr), and its analytical methodology is formulated.